delta y vs. dy (differential)

Рет қаралды 271,970

6 жыл бұрын

We will discuss the difference between delta y and dy. Delta y is the difference between y-value value and the original y-value. But dy is the differential and it's an approximated difference between the y-values.
For more calculus tutorials, please check out my just calculus channel ‪@bprpcalculusbasics‬
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Пікірлер: 357

@richardaversa7128 5 жыл бұрын

For those not aware, what he described is essentially Linear Approximation, or Linearization

@beoptimistic5853 3 жыл бұрын

kzfaq.info/get/bejne/jrd5ldFjnMqzmnk.html 💐

@rangertato Жыл бұрын

I'm pretty sure linearization is different

@richardaversa7128 Жыл бұрын

@@rangertato how so?

@rangertato Жыл бұрын

@@richardaversa7128 linearization is when you change one or both variables so that the resulting graph is linear, for example a y=1/x graph can be plotted as y vs 1/x instead of y vs x so that it can be analysed without calculus

@rayarx4213 Жыл бұрын

@@richardaversa7128linear approximation is approximation with tangent line linearization is modifying curved data to make it fit a linear line of best fit

@drachaksakcha 4 жыл бұрын

> ∆y is exact change that would explain why I never have any ∆y when I go to the coffee shop

@nevanmasterson46 4 жыл бұрын

genius pun right here, give this person a medal

@mannyheffley9551 4 жыл бұрын

Under rated

@solarsystem1958 4 жыл бұрын

??? Give an explanation please

@mannyheffley9551 4 жыл бұрын

@@solarsystem1958 del y = change

@Antonio-qe2cc 4 жыл бұрын

LMAO

@johnchristian5027 6 жыл бұрын

I like these in depth videos, they make you appreciate math more, as apposed to how you learn in high school just rushing through memorizing formulaes and rote learning solutions. Great video!

@blackpenredpen 6 жыл бұрын

Yay!! I am glad to hear this. Thank you.

@RicardoOliveiraRGB 6 жыл бұрын

Agreed, I hope he does it more and more

@ramesh.programming 3 жыл бұрын

I am happy that we have teacher who at least explained this.

@ayaanlandyn6790 2 жыл бұрын

sorry to be so offtopic but does any of you know a way to log back into an Instagram account..? I was dumb lost my account password. I would love any tips you can offer me!

@conorzayden8183 2 жыл бұрын

@Ayaan Landyn Instablaster =)

@asadashoori5553 3 жыл бұрын

I finally found out what exactly differential is. I've searched on the internet, read books for a few weeks but I couldn't find a tutorial as simple as yours. I'm gonna pray for you. Thank you so much.

@Gaark 6 жыл бұрын

and now I finally understand why there's a 'dx' tacked on the end of the dif'd function :D thanks!

@fruityliciousk2704 4 жыл бұрын

got my mind blown recently on that part. why did nobody tell me why it is there before?

@swedishpsychopath8795 5 ай бұрын

@@fruityliciousk2704 Because it is Big american secret!

@randomeggthatworksforthefb7172 3 жыл бұрын

Holy moly this was so much better than my professors explanation! He literally was trying to explain the concept using marble and bread.

@benburdick9834 6 жыл бұрын

This can be a great introduction into Euler's method as well!

@blackpenredpen 6 жыл бұрын

yup!

@animalfarm7467 6 жыл бұрын

Interesting, I always understood dy/dx only existed on the limit as Δx approached zero. Anything else was just delta Δy/Δx. ie dy/dx=lim Δx→0 Δy/Δx.

@danielschwegler5220 4 жыл бұрын

You were correct 100%. (d/dx)() is a function operator that takes a function f as its argument. f has to be a function on x. So (d/dx)(f) is the transformed function. The transformation is defined by the limit of the difference operator, just as you stated. (d/dx)(f) is the same as f'. It's just a different notation. This is ALL that makes the definition of d/dx, nothing else. There is NO multiplication by dx or dy whatsoever because d/dx() is ONE symbol. It's like if a teacher would tell you to divide both sides of the equation sin(2x)=1 by s to get in(2x)=1/s. So, what is done is symbolical manipulations that give you the name of a desired function, e.g. a solution of a differential equation. Hence it's a useful method but the method is formally not mathematical. So, those steps are no more mathematical than, let's say, you make your teacher deliver you a solution of cos(x-sin(×)+sqrt(x))=2 by threatening him to burn his dog. It's a valid and effortless method to get the solution. Once you have it, you can valit it. That threath is a non formally mathematical method just like multiplying by dx. Importantly, we need to consider why the method works. That reason is of course mathematical. In abstract Algebra operations on objects called dx are defined and it is useful. So, there differentials are from a different perspective.

@Kokurorokuko 3 жыл бұрын

yes, this is the best way to explain it.

@Davith_D 11 ай бұрын

I disagree slightly with the reply above. While (d/dx)(f) is the 'primitive' notion, its existence implies that of the differentials, and the relationship between the two is more than 'symbolical manipulations'. If y = f(x), then the differentials of x and y, 'dx' and 'dy', satisfy the equation dy = dx · f'(x) -- this makes it permissible to swap f'(x) with dy/dx (noting that dx is non-zero). It is customary for dx = Δx. The differentials are then valid objects in their own right, and f being differentiable implies their existence always -- not just 'on the limit'. The important property at the limit of dx → 0 is that Δy and dy coincide; but the value dy/dx can be considered for non-limit values of dx -- this will in general be distinct from Δy/Δx.

@lucarosolem2628 3 жыл бұрын

Mate, thank you a lot. I've been reading James Stewart's book for over an hour trying to understand what you've simplified in 10 minutes.

@Random-om8rq Жыл бұрын

Been reading Thomas Calculus on it & yea same problem.

@saranikolic2283 4 жыл бұрын

Thank you so much! I'm rewatching this video after 6 months. The idea is very clear, and the explanations were understandable. This helps me a lot. ♥

@beoptimistic5853 3 жыл бұрын

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@alegian7934 6 жыл бұрын

I love how you show real uses of theoretical calculus. Liked 😉

@JamalAhmadMalik 6 жыл бұрын

It was what I needed today.

@domrushton9651 2 жыл бұрын

Thanks mate by far the easiest explanation vid I have found on KZfaq. You must be a great tutor 👍

@HaloWolf102 2 жыл бұрын

Haven't took an intertest in Math ever, even when I was doing this in school. I always came across the Delta symbol in Wiki articles whenever I was looking up information. This defined it quite well.

@saeedgul3040 3 жыл бұрын

Impressed with the way you explained such a technical concept with sweet and smiley face Thanks

@DarkMage2k 6 жыл бұрын

That cleared out some of my back of the mind doubts

@chaosend3815 4 жыл бұрын

Thank you very much! I am revisiting this topic in Calc 3 and now I get it

@beoptimistic5853 3 жыл бұрын

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@aubreydosto1894 3 жыл бұрын

I watched your video to learn actually but I suddenly smile when you're looking and smiling at the camera. How cute of you💕

@TranquilSeaOfMath 6 ай бұрын

I like the graphs you include to assist your instruction and listener understanding.

@garybort 6 жыл бұрын

I’m stuck because I don’t have a calculator with me 😆

@iliabarani6766 Ай бұрын

Nice content man, it really helped

@MarcoYeungChannel 6 жыл бұрын

This makes my concept clear now! Thanks

@blackpenredpen 6 жыл бұрын

Yay!!

@brucefrancisyang8816 3 жыл бұрын

its very useful for me ,ive just confused by the class course ,when i saw this video ,it makes my brain clear again

@maven12LA 3 жыл бұрын

You’re a good teacher. Thanks

@gunaleswaran Жыл бұрын

Thank you sir for posting such great video .I couldn't understand what is the difference between delta and differential.But now iam Clear with that.Such a great explanation ❤

@JhonElDeSistemas 5 жыл бұрын

It's amazing your explanation. Thanks

@rokseyha1343 2 жыл бұрын

Thank you for this explanation. It really make me understand better

@soyeecheung5080 4 жыл бұрын

Bravo!! Crystal clear explanation!!

@hoteny 2 жыл бұрын

Thanks. My math teacher just wouldnt tell me what the heck was a dx or dy or d in general (only told me it was differential) This was a good explaining

@michaelnortheast394 6 жыл бұрын

Great explanation! Great video.

@josephlively2524 3 жыл бұрын

WOW! This is one of the best videos on KZfaq.

@beoptimistic5853 3 жыл бұрын

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@imranmahmood6105 3 жыл бұрын

This was a really great explanation. Thank you!

@materioverda1655 3 жыл бұрын

Very concise, very understandable. Thanks.

@bigrobbyd.6805 6 жыл бұрын

Your videos really remind me of just how much I've forgotten. :)

@smrtfasizmu6161 3 жыл бұрын

This channel is fantastic, I thought that dx and dy were delta x and delta y when delta x approaches zero. That they really make sense only when they are divided by each other and that we can sometimes use them separately but that was just a math trick. Apparently, dx and dy are not necessarily going to zero, they are just delta x and delta y of the tangent line which is determinate by the derivative. The only thing is that ratio dy/dx has to be equal to the ratio of delta y/delta x in the limit when delta x - >0.

@LynZai 2 жыл бұрын

thank you, you make it so easy to understand what exactly does "d"y mean.

@anjanasahu8416 Жыл бұрын

With the god pen switching technique he also writes so fast that I didn’t see him writing 7:04 “just an approximated” A man with so much talent !

@vankahunandareddy8093 4 жыл бұрын

Thank you sir for your clear explanation

@swedishpsychopath8795 5 ай бұрын

This is the best explanation ever! Thank you!

@agautam5208 4 ай бұрын

His geometric representation is wrong 😊 go and check mit Herbert gross lecture approximation

@tony91200211 6 жыл бұрын

This is so dope

@Nonsense116 10 ай бұрын

Excellent explanation! Thank you!

@yashagarwal3999 5 жыл бұрын

U explaination very well u were very cool throughout the video

@santoshp6376 4 жыл бұрын

thank you very much. now I actually understand what differentiation tells us.

@zunairasajid7348 4 жыл бұрын

I really appreciate your hardwork. Thank you.

@beoptimistic5853 3 жыл бұрын

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@alfonsocastillosuarez5925 3 жыл бұрын

Loved the explanation, really helped me

@beoptimistic5853 3 жыл бұрын

kzfaq.info/get/bejne/jrd5ldFjnMqzmnk.html 💐

@krypton7412 6 жыл бұрын

Thanks for making the difference clear! :)

@kirasussane1556 5 жыл бұрын

Thanks so much for these videos I can't understand math the way is teach it in school

@beoptimistic5853 3 жыл бұрын

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@vhsanson 4 жыл бұрын

Obrigado pela brilhante explicação.

@waheedbhatti7084 3 жыл бұрын

Excellent explanations.... 👌👌

@dr.rahulgupta7573 2 жыл бұрын

Excellent presentation. vow !!

@mystified_dignity 2 жыл бұрын

Very nice explanation!

@HD-vu5vv 2 жыл бұрын

Wow, nunca pensé que le entendería a lo que explicaba este man en sus videos, pero me ha servido para la tarea de cálculo xd

@intelectualoides8429 3 жыл бұрын

Great explanation!

@ganchimegganbaatar5515 4 жыл бұрын

It's very very clear now. Thank you soooooooo much

@beoptimistic5853 3 жыл бұрын

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@TheStargazer1221 2 жыл бұрын

My boi is slaying the professors with a 10$ mic.

@ghassanneamah5104 4 жыл бұрын

find dy/dx for y^-3/5=sec^-1*sqrtx* 4^lnx / y^2*lnx* tan^-1 *2x i try solving this derivatives .tanks allot

@impeun4410 4 жыл бұрын

Thank you. Keep up the good work!

@beoptimistic5853 3 жыл бұрын

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@ferxt600 4 жыл бұрын

excellent explanation, excellent

@sarwathussain9074 4 жыл бұрын

Can you please share what course are you studying. Your knowledge of calculus is soo coool

@youtubeuser2587 6 жыл бұрын

Do one with Sigma and Integral too!!

@MrStratospherestudio 4 жыл бұрын

Great video dude!

@rd-tk6js 4 жыл бұрын

Well explained !

@dr.rahulgupta7573 3 жыл бұрын

Thanks for making my concepts more clear . DrRahul Rohtak

@jasaminshirzad317 Жыл бұрын

thank you so much, so helpful 😁

@ascodes3461 3 жыл бұрын

Thank You soo much Sir

@pingueaeron 2 жыл бұрын

I was wondering if, when deriving equations such as momentum equation in aerodynamics, delta P can also be rewritten as dP since both essentially mean change in pressure?

@Chrisymcmb 3 жыл бұрын

This is amazing!

@developerg7057 Жыл бұрын

thanks, you are my math god

@Infinitesap 5 жыл бұрын

You are out off this world! Amazing understading you have. I love your videos and the way you just explains stuff my teachers never was capable of. Thanks very much.

@blackpenredpen 5 жыл бұрын

Trying to learn thank you!!

@amrgamal3613 2 жыл бұрын

Thanks mate you are amazing

@arrheniusleibniz 3 ай бұрын

dy is also a change like ∆y but this change is estimated value. Calculus can pull out very detailed information.

@hananehassine3453 3 жыл бұрын

finally i've understood the difference betwen derivatives and differential thaaaaaaanks

@ayansuleymanova03 2 жыл бұрын

Thank you sooo much!!!!!

@astrophien4253 4 жыл бұрын

This video saved my life two times

@beoptimistic5853 3 жыл бұрын

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@kharolemiliavillamontemont9769 2 жыл бұрын

Im gonna cry right now bc i got a 1.5/10 on my calc test bcz of this thing and you just made my life a lil bit better i cant thank you enough fr

@archivedinitialresearchcha1015 Жыл бұрын

Hang in there. Most of us did the same. Just keep doing limit problems...at some point, and it's different for everybody, your brain will thoroughly grasp the concept and application.

@Blendershick 4 жыл бұрын

Wow thank you very much!

@nickharrison3748 2 жыл бұрын

explaining nicely

@satyavirsinghyadav1031 5 жыл бұрын

Thanks a lot sir

@pat1x179 5 жыл бұрын

I dont even have this stuff in school rn, ( going to have it in some weeks) and I already understand smth thank u xd

@beoptimistic5853 3 жыл бұрын

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@xsamsungg5735 4 жыл бұрын

Gotta love calculus

@beoptimistic5853 3 жыл бұрын

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@piyushraj2539 3 жыл бұрын

After this awesome video 🙂😍 now I have subscribed your channel ..thank you very much sir 💙💙🇮🇳🇮🇳💙💙

@beoptimistic5853 3 жыл бұрын

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@thequestions7013 3 жыл бұрын

Thank you Sir.... A student from India... They skip this in class and say to memorize the formuals...

@williamjayaraj2244 4 жыл бұрын

Thank you.

@stellaunya5192 4 жыл бұрын

Thank you

@f.fgaming8155 2 жыл бұрын

This type of videos i want 😀

@desertrainfrog1691 2 жыл бұрын

Thanks 🤝

@preetbenipal1034 4 жыл бұрын

thank you so much ...

@marcellomarianetti1770 5 жыл бұрын

Wow thank you a lot

@blackpenredpen 5 жыл бұрын

: )

@keypo790 Жыл бұрын

d(f (x)/dx is a shortway hand of writing delta-y/delta-x when back then they used to find derivatives manually by plugging in delta-x minus h, i recall, they dont have shortcut formula for doing it, now d(f(x)/dy aka dy/dx is now used to implicitly tell that what its doing is approximation

@AB-qw4ro 3 жыл бұрын

thank you

@JossinJax 6 жыл бұрын

You rock!

@nic_von4872 Жыл бұрын

THANK YOU

@sarangabbasi2560 4 жыл бұрын

exactly what i want. THAAAAANKS!

@beoptimistic5853 3 жыл бұрын

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@rajbirvirdi4571 3 жыл бұрын

Thank you sm x

@funnyworld8947 4 жыл бұрын

兄弟，我看了你好多视频了…要是能有中文版本的就跟帅气了～

@leonyao4432 3 жыл бұрын

有中文视频，不过很少，在他频道里找找吧

@asdsliet 3 жыл бұрын

This video save my life

@mrmeowtv6248 6 жыл бұрын

I understand how you defined dy as the approximate change in y-values of the function, but can you say it is the exact change in y-value for the tangent line at the point dy/dx was calculated on y = root(x)?

@martinepstein9826 6 жыл бұрын

The way he defined it, yes. It's exactly like Delta y but for the tangent line function instead of the sqrt() function. In any calculus class you will ever take, no. dx and dy are not variables so we can't plug in numbers for dx and see what we get for dy. We can't even find values for dy and dx since they aren't numbers. They're a notation shortcut for certain equations involving limits.